Ali K. Uncu

aku21@bath.ac.uk

Publications

Publications Editorial WorkVoluntary Work

Recent Publications

  1. ArXiv A MacMahon Analysis View of 4 Diagonal DSPPs, with Runqiao Li.
  2. Autonomous first-order algebraic q-difference equations and their rational solutions, with Thieu Vo. (Accepted, ISSAC 2026)
  3. ArXiv A Weighted Words Study of MacMahon’s and Russell’s Modulo 6 Identities.
  4. ArXiv Combinatorial Proofs of Ismail’s Identities on Al-Salam–Chihara Polynomials. Arab. J. Math. (2026).
  5. ArXiv A MacMahon Analysis View of Cylindric Partitions, with Runqiao Li. Ramanujan Journal Volume 68, Article 71 (2025).- Documentation worksheet: .nb and .pdf
  6. ArXiv Quantifier Elimination for Normal Cone Computations, with Michael Mandlmayr, Journal of Symbolic Computation Volume 131, Nov-Dec 2025, 102456 – Documentation worksheet: .nb and .pdf
  7. ArXiv Iterated Resultants and Rational Functions in Real Quantifier Elimination, with James H. Davenport, Matthew England, and Scott McCallum. Mathematics in Computer Science vol 19, 12 (2025).
  8. ArXiv Factorial Basis Method for q-Series Applications, with Antonio Jimenez-Pastor. ISSAC ’24: Proceedings of the 2024 International Symposium on Symbolic and Algebraic Computation382–390 (2024).
  9. ArXiv A Poly-algorithmic Approach to Quantifier Elimination, with James H. Davenport, and Zak P. Tonks. 25th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC), Nancy, France, (2023), pp. 44-51
  10. ArXiv Lazard-style CAD and Equational Constraints, with James H. Davenport, Akshar Nair, and Gregory Sankaran. ISSAC ’23: Proceedings of the 2023 International Symposium on Symbolic and Algebraic Computation 218–226.
  11. ArXiv A Unified Approach to Unimodality of Gaussian Polynomials, with Christoph Koutschan and Elaine Wong. ISSAC ’23: Proceedings of the 2023 International Symposium on Symbolic and Algebraic Computation 434–442 (2024).
  12. ArXiv Proofs of Modulo 11 and 13 Cylindric Kanade-Russell Conjectures for A_2 Rogers-Ramanujan Type Identities (submitted) Documentation
  13. ArXiv Sequences in Overpartitions, with George E. Andrews. Ramanujan J. Volume 61, pages 715–729, (2023) .
  14. IEEE Artificial Conflict Sampling for Real Satisfiability Problems, with James H. Davenport 24th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC) 2022, IEEE Electronic Publication Paper Id: 1668357797545
  15. CEUR-WS SMT-Solving Induction Proofs of Inequalities, with James H. Davenport and Matthew England, In SC-Square 2021: Satisfiability Checking and Symbolic Computation (CEUR Workshop Proceedings, Vol. 3458), CEUR, 10-24 (2023).
  16. ArXiv On Finite Analogs of Schmidt’s Problem and Its Variants, with Alexander Berkovich. Séminaire Lotharingien de Combinatoire 88 (2023), Article B88b, 18 pp
  17. ArXiv Weighted Cylindric Partitions, with Walter Bridges. Journal of Algebraic Combinatorics volume 56, pages 1309–1337 (2022)
  18. CEUR-WS Practical Evaluation of Quantifier Elimination Methods, with James H. Davenport, and Zak P. Tonks. In SC-Square 2021: Satisfiability Checking and Symbolic Computation (CEUR Workshop Proceedings, Vol. 3273), CEUR, 41–49 (2022).
  19. ArXiv New infinite hierarchies of polynomial identities related to the Capparelli partition theorems, with Alexander Berkovich. J. Math. Anal. Appl. 506 (2022), no. 2, Paper No. 125678, 18 pp.
  20. ArXiv Cylindric Partitions and some new A_2 Rogers-Ramanujan Identities, with Sylvie Corteel and Jehanne Dousse. Proc. Amer. Math. Soc. 150 (2022), 481-497.
  21. ArXiv Reflecting (on) the modulo 9 Kanade-Russell (conjectural) identities, with Wadim Zudilin. Séminaire Lotharingien de Combinatoire 85 (2021), Article B85e, 17 pp
  22. ArXiv On Double Sum Generating Functions in Connection with Some Classical Partition Theorems. Disc. Math J. Volume 344, Issue 11, (2021), 112562
  23. ArXiv qFunctions – A Mathematica package for q-series and partition theory applications, with Jakob Ablinger. Journal of Symbolic Computation 107 (2021), 145-166.
  24. ArXiv Logconcavity results for a biparametric and an elliptic extension of the q-binomial coefficients, with Michael Schlosser and  Koushik Senapati. Int. J. Number Theory 17 (2021), no. 3, 787–804.
  25. ArXiv Where do the maximum absolute q-series coefficients of (1-q)(1-q^2)(1-q^3)\dots(1-q^{n-1})(1-q^n) occur?, with Alexander Berkovich. Experimental Mathematics, 32:1, 82-87, (2023) DOI: 10.1080/10586458.2020.1776177 (Online first 2020)
  26. ArXiv On a weighted spin of the Lebesgue Identity. Mathematical Aspects of Computer and Information Sciences. MACIS 2019. Lecture Notes in Computer Science, vol 11989. Springer, Cham. https://doi.org/10.1007/978-3-030-43120-4_20
  27. ArXiv A Polynomial Identity Implying Schur’s Partition Theorem. Proc. Amer. Math. Soc. 148 (2020), 3307-3324
  28. ArXiv Refined q-Trinomial Coefficients and Two Infinite Hierarchies of q-Series Identities, with Alexander Berkovich. Algorithmic Combinatorics: Enumerative Combinatorics, Special Functions and Computer Algebra. Texts & Monographs in Symbolic Computation (A Series of the Research Institute for Symbolic Computation, Johannes Kepler University, Linz, Austria). Springer, Cham. https://doi.org/10.1007/978-3-030-44559-1_4
  29. ArXiv Elementary Polynomial Identities Involving q-Trinomial Coefficients, with Alexander Berkovich. Ann. Comb. 23 (2019), 549–560.
  30. ArXiv Polynomial Identities Implying Capparelli’s Partition Theorems, with Alexander Berkovich. J. Number Theory 201 (2019), 77-107.
  31. ArXiv Some Elementary Partition Inequalities and Their Implications, with Alexander Berkovich. Ann. Comb. 23 (2019), 263-284.
  32. ArXiv Weighted Rogers-Ramanujan Partitions and Dyson Crank.  Ramanujan J. 46 (2018), no. 2, 579–591.
  33. ArXiv On Some Polynomials and Series of Bloch-Polya Type, with Alexander Berkovich. Proc. Amer. Math. Soc. 146 (2018), no. 7, 2827–2838.
  34. ArXiv New Weighted Partition Theorems with the Emphasis on the Smallest Part of Partitions, with Alexander Berkovich. ALLADI 60 2016: Analytic Number Theory, Modular Forms and q-Hypergeometric Series (2017) pp 69-94 Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 221)
  35. ArXiv Variation on a theme of Nathan Fine. New weighted partition identities, with Alexander Berkovich. J. Number Theory 176 (2017), 226–248.
  36. ArXiv On partitions with fixed number of even-indexed and odd-indexed odd parts, with Alexander Berkovich. J. Number Theory 167 (2016), 7–30.
  37. ArXiv A New Companion to Capparelli’s Identities, with Alexander Berkovich. Adv. in Appl. Math. 71 (2015), 125–137.

Extended Abstracts

  1. qFunctions: A Mathematica package for partition theory applications, and its future, Computer Algebra in Scientific Computing 2021 (CASC 21) Proceedings.
  2. ArXiv The DEWCAD Project: Pushing Back the Doubly Exponential Wall of Cylindrical Algebraic Decomposition, with Russell Bradford, James H. Davenport, Matthew England, and Amirhossein Sadeghimanesh. ISSAC 2021 https://dl.acm.org/doi/abs/10.1145/3511528.3511538
  3. On q-Rising Factorials and the Necessity of Shared Memory Calculations. Austrian High-Performance-Computing meeting (AHPC2020), Publisher: Institute of Science and Technology Austria, Klosterneuburg Austria, Editors: Alois Schlögl et al. ISBN: 978-3-99078-004-6

Databases

Popular Math Publications

  1. Parçalanış Teorisine Davet, Matematik Dünyası Yıl 29, Sayı 119, Aralık 2022 (Eng. Invitation to Theory of Partitions, World of Mathematics Journal, year 29, vol 119, December 2022)

Editorial Work

I am the Managing Editor of Journal of Algebraic Combinatorics since 06/2026. I have been an associate editor at the Mathematics in Computer Science since 01/2023.

  1. Editor: 7th SC^2 Workshop Proceedings (SC^2 2022) with Haniel Barbosa.
    CEUR-WS (2023) Here is its Preface
  2. Guest Editor: Mathematics in Computer Science – ACA 2022 Special Issue, with Tülay Ayyıldız Akoğlu, Ilias Kotsireas and Zafeirakis Zafeirakopoulos, published by Birkhauser Springer.
  3. Guest Editor: Mathematics in Computer Science – ACA 2021 (Virtual Online) Special Issue, with Ilias Kotsireas and Dimitris Simos, published by Birkhauser Springer.
    Here is its Foreword

Other Voluntary Work

A list of journals for which I wrote reports for can be found here.

Reviewer for American Mathematical Society MathSciNet.

Judge at MAA Committee on Undergraduate poster session at JMM 2019 and 2020.

Judge at CMS Summer Meeting 2021 Undergraduate poster session.